Well, that looked interesting, and the HC1 boss looked hard :-)
It would also be pretty frustrating as there might be many situations where you have only one try and no chance to suicide to re-attempt the level.
Another idea, mainly inspired by Master Blue:
Finish a S1/S2/S3/S%K (your choice) in 5 minutes. You gain an additional 5 (10?) seconds for each monitor you opened. This would force players to play fast but they canÂ´t take the standard routes.
There are also many variations of this theme, like giving different time bonuses for different monitors (e.g. extra life = 30 seconds, ring box = 0 seconds, etc.).